Effects of Grain Size and Doping Level on the Critical Current Density of the Ti-sheathed MgB$_{2}$ Superconducting Wires with SiC Doping

The effects of the grain size and doping level on the critical current density ($J_{c})$ of the SiC-doped Ti-sheathed MgB$_{2}$ superconducting wires were studied. Two groups of samples were prepared: for the first group, the average size of the SiC grains was 20 nm and the doping levels were 5{\%}, 10{\%}, and 15{\%}; for the second group, the doping level of the SiC dopant was 10{\%} and the average sizes of the SiC particles were 20 nm, 43 nm, and 123 nm. All of the samples were sintered at 800 C for 30 minutes. Contrary to the $J_{c}$ results reported on the SiC-doped Fe-sheathed MgB$_{2}$ wires by some other groups, we found that the $J_{c}$ for the SiC-doped Ti-sheathed MgB$_{2}$ wires decreases with both the increase of SiC concentration and the decrease of the grain size. Only for the wires with average grain size of 123 nm, $J_{c}$ is greater than that of the un-doped MgB$_{2}$ wires. A simple model is proposed to explain the formation of the impurities in the cores of these doped MgB$_{2}$ wires. This unusual dependence of $J_{c}$ on the size and doping-level of the SiC dopant is discussed in association with the magnetization, resisitivity, XRD, TEM, and SEM results.